Robust transitivity of singular hyperbolic attractors
Dynamical Systems
2020-01-22 v1
Abstract
Singular hyperbolicity is a weakened form of hyperbolicity that has been introduced for vector fields in order to allow non-isolated singularities inside the non-wandering set. A typical example of a singular hyperbolic set is the Lorenz attractor. However, in contrast to uniform hyperbolicity, singular hyperbolicity does not immediately imply robust topological properties, such as the transitivity. In this paper, we prove that open and densely inside the space of vector fields of a compact manifold, any singular hyperbolic attractors is robustly transitive.
Keywords
Cite
@article{arxiv.2001.07293,
title = {Robust transitivity of singular hyperbolic attractors},
author = {Sylvain Crovisier and Dawei Yang},
journal= {arXiv preprint arXiv:2001.07293},
year = {2020}
}